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If [tex]\( f(x) = 2x^2 + 5\sqrt{x-2} \)[/tex], complete the following statement:

[tex]\[ f(6) = \][/tex]

[tex]\[
\text{Answer here:} \quad \_\_\_\_\_
\][/tex]

Sagot :

GinnyAnswer
To find [tex]\( f(6) \)[/tex] for the function [tex]\( f(x) = 2x^2 + 5\sqrt{x - 2} \)[/tex], follow these steps:

1. Substitute [tex]\( x = 6 \)[/tex] into the function:
[tex]\[ f(6) = 2(6)^2 + 5\sqrt{6 - 2} \][/tex]

2. Calculate [tex]\( (6)^2 \)[/tex]:
[tex]\[ (6)^2 = 36 \][/tex]

3. Multiply [tex]\( 2 \)[/tex] by [tex]\( 36 \)[/tex]:
[tex]\[ 2 \times 36 = 72 \][/tex]

4. Calculate [tex]\( 6 - 2 \)[/tex]:
[tex]\[ 6 - 2 = 4 \][/tex]

5. Find the square root of [tex]\( 4 \)[/tex]:
[tex]\[ \sqrt{4} = 2 \][/tex]

6. Multiply [tex]\( 5 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[ 5 \times 2 = 10 \][/tex]

7. Add the two results together:
[tex]\[ 72 + 10 = 82 \][/tex]

Therefore, [tex]\( f(6) = 82 \)[/tex].
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